DEPLETION OF NONLINEARITY FOR SPACE-ANALYTIC SPACE-PERIODIC SOLUTIONS TO EQUATIONS OF THE HYDRODYNAMIC TYPE

We consider solenoidal space-periodic space-analytic solutions to the equations of hydrodynamics. An elementary bound shows that due to the special structure of the nonlinear terms in the equations for modified solutions, effectively they lack a half of the spatial gradient. This appears to be a novel mechanism for depletion of nonlinearity. We present a two-phase iterative procedure yielding an expanded bound for the guaranteed time of the space analyticity of the hydrodynamic solutions.